Laid-open specification WO 00/67294 describes a high-pressure discharge lamp for motor vehicle headlamps having a ceramic discharge vessel which has an internal diameter of less than 2 mm and in which there is an ionizable fill. The ionizable fill comprises xenon, mercury and metal halides, in particular iodides of the metals sodium and cerium, and also, if appropriate, iodides of the metals calcium and dysprosium.